Motivated by strong theoretical guarantees regarding estimation and structure learning induced by the Horseshoe prior in a regression model [1]}, [2]}, [3]}, we propose to investigate the performance of the same in our fusion estimation framework. The Horseshoe prior induces sparsity via an infinite spike at zero, and also possess a heavy tail to ensure consistent selection of the underlying pieces or blocks. Furthermore, the global scale parameter that controls the level of sparsity in the model automatically adapts to the actual level of sparsity in the true model, as opposed to choosing the scale parameter in the \(t\) -shrinkage prior on the basis of the underlying dimension \(n\) . The conjugate structure of the posterior distribution arising out of modeling via a Horseshoe prior allows fast computation along with working with the full posterior distribution, so that the samples obtained via Markov Chain Monte Carlo (MCMC) can further be used for uncertainty quantification.
